Simplify the following expression: $ a = \dfrac{4}{9} - \dfrac{-4}{9r - 2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9r - 2}{9r - 2}$ $ \dfrac{4}{9} \times \dfrac{9r - 2}{9r - 2} = \dfrac{36r - 8}{81r - 18} $ Multiply the second expression by $\dfrac{9}{9}$ $ \dfrac{-4}{9r - 2} \times \dfrac{9}{9} = \dfrac{-36}{81r - 18} $ Therefore $ a = \dfrac{36r - 8}{81r - 18} - \dfrac{-36}{81r - 18} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{36r - 8 + 36 }{81r - 18} $ Distribute the negative sign: $a = \dfrac{36r - 8 + 36}{81r - 18}$ $a = \dfrac{36r + 28}{81r - 18}$